Pricing Alternative forms of Commercial insurance cover. Andrew Harford

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1 Pricing Alternative forms of Commercial insurance cover Andrew Harford

2 Pricing alternative covers Types of policies Overview of Pricing Approaches Total claim cost distribution Discounting Cash flows Adjusting quote for differences in cover Conclusion

3 Conventional Policies where insurer only pays some claims Aggregate XOL Policies involving premium adjustments Burner CED Types of Policy

4 Pricing alternative covers Types of policies Overview of Pricing Approaches Total claim cost distribution Discounting Cash flows Adjusting quote for differences in cover Conclusion

5 Role of underwriter Quote for conventional Exposure Claim experience Changes over time Breakdown of premium Expected claim number and size Expenses Cost of reinsurance Profit

6 Pricing approaches Aggregates and XOLs - insurer does not pay all claims and receives fixed premium CEDs and Burners - insurer pays all claims but there are premium adjustments Different approach required for the two groups: Adjusting for differences in cover Discounting expected cash flow

but there are premium adjustments Different approach required for the

7 Pricing alternative covers Types of policies Overview of Pricing Approaches Total claim cost distribution Discounting Cash flows Adjusting quote for differences in cover Conclusion

8 Distribution of total claim cost Need a distribution of total claim costs: T=X 1 + X X N For aggregate need it to assess cost of claims over aggregate limit For Burners and CEDs also need this distribution Derive using assumptions about distribution of claim numbers and claim sizes

9 Claim number distributions Choose the form of the distribution: Poisson, Negtive binomial, Choose parameters of the distribution Set expected value equal to underwriters assessment Model different clam types separately

parameters of the distribution Set expected value

10 Claim size distributions Choose the form - Lognormal, Gamma, Test validity of selection Use underwriter s assessment to set mean How to set variance? Sigma Parameter Mu Parameter

assessment to set mean How to set variance?

11 Simulation Quick with modern computing power Simple to implement Easy to understand Flexible - Calculate other items of interest

12 Other considerations Development delays Model and parameter uncertainty Accumulations

13 Pricing alternative covers Types of policies Overview of Pricing Approaches Total claim cost distribution Discounting Cash flows Adjusting quote for differences in cover Conclusion

14 Discounting expected cash flows Burners and CEDs insurer pays all claims Premium adjustments depending on claims Simulate potential claims for a year and the premium adjustments they generate Calculate the expected value of future premium adjustments Discount expected premium adjustments and make equal to Conventional quote

premium adjustments they generate Calculate the expected value of future premium

15 Discounting expected cash flows Considerations : credit rating of insured development of claims Uncertainty in constructing claim distributions

16 Pricing alternative covers Types of policies Overview of Pricing Approaches Total claim cost distribution Discounting Cash flows Adjusting quote for differences in cover Conclusion

17 Adjusting for differences in cover Underwriter produces quote for conventional policy Start of with underwriters assessment and adjust for differences in cover

18 Adjusting for differences in cover

19 Adjusting for differences in cover Suitable for Aggregates and XOLs Ensures consistency with underwriter s quote Relies on skill of underwriter

20 Expected cost of claims For aggregate compute Max(T-A,0) in each simulation and get average

21 Claims handling Expenses Claims handled by client or insurer? Underwriting Time involved preparing quote Overheads

22 Reinsurance Reinsurance recoveries calculated for each simulation for the conventional and the alternative risk Derive ratio for average recovery from conventional and from alternative Apply this ratio to reinsurance margin in conventional quote

23 Investment income Delays in paying claims: Typically involves larger claims Not usually material on short tail lines

24 No consensus Profit Consider level of capital needed for conventional policy versus capital for alternative policy Benchmark game theoretic approach Average amount of marginal capital needed to write risk difficult to apply in practice

25 Profit some approaches Standard deviation Value at risk Probability of meeting claims to some level Proportional hazards Capital consumption

26 Profit comparison of methods 100% How the ratio for each method varies with the Aggregate limit 80% Ratio 60% 40% 20% 0% Aggregate limit Aggregate cost as a percentage of conventional cost Method 2-99% probability Method 3 - VAR Method 4 - PH transform, r=0.95 Method 1 - based on standard deviation Method 2-98% probability Method 4 - PH transform, r=0.8 Benchmark - Equal probability of insolvency

27 Pricing alternative covers Types of policies Overview of Pricing Approaches Total claim cost distribution Discounting Cash flows Adjusting quote for differences in cover Conclusion

28 Conclusion Modifying the underwriter s quote Consistency Tractability Simplifies some of the calculations Use knowledge & skill of underwriter

Pricing Alternative forms of Commercial Insurance cover

Pricing Alternative forms of Commercial Insurance cover Prepared by Andrew Harford Presented to the Institute of Actuaries of Australia Biennial Convention 23-26 September 2007 Christchurch, New Zealand